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Path through a 3x3x3 grid
Posted:
Feb 20, 2013 10:40 AM
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There is a (well known) continuous path, made of four straight
sections, which passes exactly once through each of 9 points arranged
in a square 3x3 array.
Using three of these paths, plus two plane-to-plane straight sections,
it is clearly possible to make a continuous path, made of 14 straight
sections, which passes exactly once through each of 27 points arranged
in a 3x3x3 grid.
However, there is at least one such path made up of only straight 13
sections.
Can you find such a path?
Suggested notation:
The grid consists of all points (x,y,z) with x, y and z being integers
satisfying 0 <= x, y, z <= 2. For a path, give the starting point and
all subsequent "target points".
So a path might begin:
(0, 0, 2)
(-2, 2, 0)
...
--
Clive Tooth
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